S3-pairs and Dehn surgery on knots

Abstract

Two general ways are explained to produce pairs of knots K, K′ in S3 and a γ ∈ Q such that the γ surgery of K coincides with the ±γ surgery of K′. They are similar in that the key ingredient in the construction is an S3-pair, a pair of framed knots whose surgery yields S3. They generalize some techniques in the literature, and give plenty of flexibility on choosing both the knots and their framings. Examples are given with a focus on a special case that works for 0 surgeries of many ribbon knots.